Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

F. Bianchi - Y. Okuyama

Degeneration of quadratic polynomial endomorphisms to a Hénon map

created by bianchi on 12 May 2018
modified on 29 Mar 2024


Published Paper

Inserted: 12 may 2018
Last Updated: 29 mar 2024

Journal: Indiana University Mathematics Journal
Volume: 69
Pages: 2549-2570
Year: 2020
Doi: 10.1512/iumj.2020.69.8092

ArXiv: 1803.10471 PDF


For an algebraic family $(f_t)$ of regular quadratic polynomial endomorphisms of $\mathbb{C}^2$ parametrized by $\mathbb{D}^*$ and degenerating to a H\'enon map at $t=0$, we study the continuous (and indeed harmonic) extendibility across $t=0$ of a potential of the bifurcation current on $\mathbb{D}^*$ with the explicit computation of the non-archimedean Lyapunov exponent associated to $(f_t)$. The individual Lyapunov exponents of $f_t$ are also investigated near $t=0$. Using $(f_t)$, we also see that any H\'enon map is accumulated by the bifurcation locus in the space of quadratic holomorphic endomorphisms of $\mathbb {P}^2$.

Credits | Cookie policy | HTML 5 | CSS 2.1